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A department manager distributed a number of books, calendars, and diaries among the staff in the department, with each staff member receiving x books, y calendars, and z diaries. How many staff members were in the department?

(1) The numbers of books, calendars, and diaries that each staff member received were in the ratio 2:3:4, respectively.(2) The manager distributed a total of 18 books, 27 calendars, and 36 diaries.

Re: A department manager distributed a number of books, calendars, and dia [#permalink]

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24 Feb 2016, 05:17

Bunuel wrote:

A department manager distributed a number of books, calendars, and diaries among the staff in the department, with each staff member receiving x books, y calendars, and z diaries. How many staff members were in the department?

(1) The numbers of books, calendars, and diaries that each staff member received were in the ratio 2:3:4, respectively.(2) The manager distributed a total of 18 books, 27 calendars, and 36 diaries.

We do not get much from the question stem, except the fact that x, y and z have to be positive integers as they represent books, calendars, and diaries respectively.Let us now consider the statements:Statement 1:This statement gives us the ratio of books, calendars, and diaries that each staff member received. This clearly is insufficient. We cannot figure out the number of staff members from this statement. It could be 10 or 1000 or even more.

So, options A and D are out.

Statement 2:If you look at this statement, it basically provides you the same information as Statement 1. 18 books, 27 calendars, and 36 diaries distributed to all staff member means that each staff member must have received books, calendars, and diaries in the ratio 2:3:4, respectively.However, this also gives us real numbers.But this statement is still insufficient as the staff members could be 3 or 9.Hence, option C is out

As mentioned above, statement 2 already contains the part of the information provided in Statement 1, there is no point looking at these statements together. Hence, even option D is out.

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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

A department manager distributed a number of books, calendars, and diaries among the staff in the department, with each staff member receiving x books, y calendars, and z diaries. How many staff members were in the department?

(1) The numbers of books, calendars, and diaries that each staff member received were in the ratio 2:3:4, respectively.(2) The manager distributed a total of 18 books, 27 calendars, and 36 diaries.

In the original condition, there are 4 variables(the number of x,y,z, staffs), which should match with the number of equations. So you need 4 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer.When 1) & 2), n=1, x=18, y=27, z=36/ n=3, x=6, y=9, z=12, which is not unique and not sufficient.Therefore, the answer is E.

 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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Considering both the statements together can result in two solutions. One, as you correctly mentioned, 9 staff members such that each received 2 books, 3 calendars and 4 diaries (a ratio of 2:3:4). Second, 3 staff members such that each received 6 books, 9 calendars and 12 diaries (again, a ratio of 2:3:4). Therefore, both the statements even when taken together is not sufficient to find a unique solution. Hope this helps!!

Re: A department manager distributed a number of books, calendars, and dia [#permalink]

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22 Oct 2017, 09:42

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